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    Weyl's inference from spherical embedding geometry to clo... — Carmelics
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    Challenges→In de Sitter's solution, space is closed in a topological sense.

    Weyl's inference from spherical embedding geometry to closed topology conflates the geometry of a particular coordinatization with intrinsic topological structure.

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    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Coordinate systems are human constructs; a sphere embedding in ℝ³ depends on choice of ambient space, not intrinsic geometry.
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    • 2.Intrinsic topology (via metric) can be defined without embedding; closedness should follow from geodesic structure alone, not extrinsic visualization.
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    • 3.A manifold can be topologically closed yet embed in higher dimensions with open coordinate domains; embedding ≠ intrinsic property.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Spherical embedding directly reveals the closed geodesic property: great circles return to start. This is intrinsic data, not coordinatization artifact.
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    • 2.The distinction between 'coordinatization' and 'intrinsic structure' breaks down in differential geometry; metrics ARE coordinate-dependent representations of intrinsic facts.
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    • 3.Weyl inferred closedness from the metric structure (constant curvature), not merely from visual embedding; the geometry itself determines topology.
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    Related

    A manifold can be topologically closed yet embed in higher dimensions with open ...Coordinate systems are human constructs; a sphere embedding in ℝ³ depends on cho...In de Sitter's solution, space is closed in a topological sense.Intrinsic topology (via metric) can be defined without embedding; closedness sho...
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    Spherical embedding directly reveals the closed geodesic property: great circles...The distinction between 'coordinatization' and 'intrinsic structure' breaks down...Weyl inferred closedness from the metric structure (constant curvature), not mer...

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    Perspectives
    2 (1 for, 1 against)
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